Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field

We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the stationary limit. If magnetic field is smaller compared to the critical value, determined by frictional anisotropy, the relaxation of the correlation is non-oscillating in time. However, in a larger magnetic field this relaxation becomes oscillating. The phenomenon is related to the statistical dependence of the components of transformed random force caused by the simultaneous influence of magnetic field and anisotropic dissipation.     

Dependence of the magnetization relaxation time of single-domain ferromagnetic particles on damping in the Brown model

Analytical expressions for the magnetization relaxation time τ of single-domain ferromagnetic particles with cubic or uniaxial anisotropy in a static transverse magnetic field are derived. The derivation is based on calculating the escape rate of a Brownian particle from a potential well; this technique is applicable at any damping and is generalized to the case of magnetic relaxation of superparamagnetic particles. The validity of the expressions obtained for τ is checked against a numerical solution of the Landau-Lifshitz-Gilbert equation over the whole range of damping (very low, intermediate, and high damping and the crossover region between low and intermediate damping).     

Lattice Boltzmann simulation of the two-dimensional flow of a magnetic suspension between two parallel walls under a non-uniform magnetic field

We have developed a lattice Boltzmann method based on fluctuation hydrodynamics that is applicable to the flow problem of a particle suspension. In this method, we have introduced the viscosity-modifying method, rather than the velocity-scaling method, in which a modified viscosity is used for generating random forces in lattice Boltzmann simulations. The viscosity-modifying method is found to be applicable to the simulation of a magnetic particle suspension. We have applied this method to the two-dimensional Poiseuille flow of a magnetic suspension between two parallel walls in order to investigate the behavior of magnetic particles in a non-uniform applied magnetic field. From the results of the snapshots, the pair correlation function between the magnetic pole and the magnetic particles and the averaged local particle velocity and magnetization distributions, it was observed that the behavior of the magnetic particles changes significantly depending upon which factor dominates the phenomenon in the balance between the magnetic particle–particle interaction, the non-uniform applied magnetic field and the translational and rotational Brownian motion.     

Magnetic properties of CoFeRu alloys in the f.c.c. and h.c.p. phases

Measurements have been made of the magnetization, the Fe⁵⁷ Mössbauer effect, and the crystal structures of Co-rich CoFeRu alloys. The alloys with f.c.c. structure behave in a typical ferromagnetic way, while those with h.c.p. structure show non-saturation of the magnetization in magnetic fields as high as 80 kG, and they show relatively small magnetic moments per atom and a broad single Mössbauer absorption.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

Dynamics of paramagnetic agents by off-resonance rotating frame technique

Off-resonance rotating frame technique offers a novel tool to explore the dynamics of paramagnetic agents at high magnetic fields (B0 > 3T). Based on the effect of paramagnetic relaxation enhancement in the off-resonance rotating frame, a new method is described here for determining the dynamics of paramagnetic ion chelates from the residual z-magnetizations of water protons. In this method, the dynamics of the chelates are identified by the difference magnetization profiles, which are the subtraction of the residual z-magnetization as a function of frequency offset obtained at two sets of RF amplitude omega(1) and pulse duration tau. The choices of omega(1) and tau are guided by a 2-D magnetization map that is created numerically by plotting the residual z-magnetization as a function of effective field angle theta and off-resonance pulse duration tau. From the region of magnetization map that is the most sensitive to the alteration of the paramagnetic relaxation enhancement efficiency R(1rho)/R1, the ratio of the off-resonance rotating frame relaxation rate constant R(1rho) verse the laboratory frame relaxation rate constant R(1), three types of difference magnetization profiles can be generated. The magnetization map and the difference magnetization profiles are correlated with the rotational correlation time tauR of Gd-DTPA through numerical simulations, and further validated by the experimental data for a series of macromolecule conjugated Gd-DTPA in aqueous solutions. Effects of hydration water number q, diffusion coefficient D, magnetic field strength B0 and multiple rotational correlation times are explored with the simulations of the magnetization map. This method not only provides a simple and reliable approach to determine the dynamics of paramagnetic labeling of molecular/cellular events at high magnetic fields, but also a new strategy for spectral editing in NMR/MRI based on the dynamics of paramagnetic labeling in vivo.     

On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Fast-field-cycling NMR study of magnetomechanically induced relaxation enhancement in ferrogelatine

We describe a field-cycling magnetic resonance experiment aimed to study the nuclear spinlattice relaxation in the simultaneous presence of an oscillating magnetic field and a magnetomechanically induced perturbation across the sample volume. The studied system is a gelatine doped with surfacted nanosize ferromagnetic particles. The spin system relaxes in coexistence with the magnetic interaction between the dopants and a weak external alternating magnetic field. Due to the interaction between the alternating field and the high magnetic moment of the dopants, a mechanical shaking of the particles becomes effective at low evolution fields. In this way, the particles act as local sonic sources, thus transmitting the vibrations to the gelic matrix where they are trapped. The impact produced on the molecular dynamics is observed through a magnetic resonance relaxation experiment. Saturation of the proton magnetization produced by the alternating magnetic field is also discussed. Results are compared with the direct effects produced by a pure sonic perturbation at the same frequency, introduced by coupling a piezoelectric transducer in direct contact with the sample.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Effect of a dc magnetic field on the magnetization relaxation of uniaxial single-domain ferromagnetic particles driven by a strong ac magnetic field

The nonlinear ac stationary response of the magnetization of noninteracting uniaxial single-domain ferromagnetic particles acted on by superimposed dc and ac magnetic fields applied along the anisotropy axis is evaluated from the Fokker-Planck equation, expressed as an infinite hierarchy of recurrence equations for Fourier components of the relaxation functions governing longitudinal relaxation of the magnetization. The exact solution of this hierarchy comprises a matrix continued fraction, allowing one to evaluate the ac nonlinear response and reversal time of the magnetization. For weak ac fields, the results agree with perturbation theory. It is shown that the dc bias field changes substantially the magnetization dynamics leading to new nonlinear effects. In particular, it is demonstrated that for a nonzero bias field as the magnitude of the ac field increases the reversal time first increases and having attained its maximum at some critical value of the ac field, decreases exponentially.     

Longitudinal dynamic susceptibility of superparamagnetic particles with cubic anisotropy

We study the linear response of a system of single-domain ferromagnetic particles with cubic magnetic anisotropy to a weak external a.c. magnetic field. By averaging the Gilbert equation with a fluctuating field for the magnetization of an individual particle we derive a system of recurrence equations for the spectra of equilibrium correlation functions describing the longitudinal relaxation of the system. We find the solution of this system by using matrix continued fractions. We also evaluate the longitudinal relaxation time and the spectrum of the complex-valued magnetic susceptibility. Finally, we show that the nature of susceptibility dispersion is determined by the anisotropy and dissipation parameters. Zh. éksp. Teor. Fiz. 115, 101–114 (January 1999)     

Brownian dynamics simulations of a cubic haematite particle suspension with a more effective treatment of steric layer interactions

We have proposed a new repulsive layer model for describing the interaction between steric layers of coated cubic particles. This approach is an effective technique applicable to particle-based simulations such as a Brownian dynamics simulation of a suspension composed of cubic particles. 3D Brownian dynamics simulations employing this repulsive interaction model have been performed in order to investigate the equilibrium aggregate structures of a suspension composed of cubic haematite particles. It has been verified that Brownian dynamics employing the present steric interaction model are in good agreement with Monte Carlo results with respect to particle aggregate structures and particle orientational characteristics. From the viewpoint of developing a surface modification technology, we have also investigated a regime change in the aggregate structure of cubic particle in a quasi-2D system by means of Brownian dynamics simulations. If the magnetic particle–particle interaction strength is relatively strong, in zero applied magnetic field the particles aggregate in an offset face-to-face configuration. As the magnetic field strength is increased, the offset face-to-face structure is transformed into a more direct face-to-face contact configuration that extends throughout the whole simulation region.     

Nonlinear response of superparamagnetic particles to a sudden change of a high constant magnetic field

For a system of superparamagnetic particles in a high external constant magnetic field, a technique for calculating the nonlinear response to a sudden change in the field direction and magnitude is proposed. A set of momentary equations for the averaged spherical harmonics, which is derived from the Fokker-Planck equation for the magnetization-orientation distribution function is the basis of this technique. As an example, the nonlinear response of a system of particles with anisotropy of the easy-axis type is examined. For this case, a solution to the momentary equations is obtained by using matrix continued fractions. The magnetization relaxation time and the spectrum of the relaxation function are calculated for typical values of anisotropy, dissipation, and nonlinearity parameters. It is shown that the magnetization kinetics is essentially dependent on these parameters.     

Application of the Brownian dynamics method to a rod-like hematite particle dispersion

We have investigated various problems that arise in applying the Brownian dynamics method to a suspension composed of rod-like hematite particles, which have a magnetic moment normal to the particle axis direction. The accuracy and the deviation of simulation results from theoretical solutions have been discussed by comparison with the theoretical solutions that were obtained by solving the basic equations of the orientational distribution function. The characteristics of the negative viscosity are not observed to be dependent on a time interval unless a sufficiently short time interval is used. The present simulation results can satisfactorily reproduce the qualitative characteristics of the negative magneto-rheological effect that was predicted by the previous theoretical investigation. Good quantitative agreement is obtained in the range of small-applied magnetic fields, but agreement is not significantly good in the large magnetic field region. The deviation of the negative viscosity from the theoretical prediction cannot be improved by using a more accurate numerical algorithm such as moving from Euler to second-order or fourth-order Runge–Kutta. The results of the orientational distribution can well reproduce the characteristic features that the distribution has a gradual shape with low linear-like peak, which is in significant contrast to the sharp single-peak distribution of a ferromagnetic rod-like particle dispersion. The present orientational distributions are in significantly good agreement with those of the theoretical prediction in regard to the position and the height of a peak and the general shape of the overall profile. Good agreement of the present magnetisation curves with the theoretical prediction verifies that the spin rotational Brownian motion is activated at a physically reasonable level in the present simulations.     

Magnetization reversal of small particles in an oscillating magnetic field

The nonlinear behavior of single spherical particles and many-particle ensembles under an external oscillating magnetic field was studied using the Landau-Lifshitz-Gilbert approach. The exact analytical formulae for calculating field frequency and the dependence of the configuration of the initial moment on the system mean magnetization were obtained. Using asymptotic decomposition we obtained simple expressions for describing the nonlinear dynamics of spherical particles in the cases of large and small frequencies. These solutions are in good agreement with numerical calculations of the Landau-Lifshitz-Gilbert equation for the considering systems.     

Effects of oscillatory shear flow on chain-like cluster dynamics in ferrofluids without magnetic fields

Brownian dynamics simulations of interacting magnetic particles in a quasi-two-dimensional ferrofluid system are performed at zero temperature, under the influence of oscillatory shear flow in the absence of external magnetic fields. Starting from chain-like clusters of the particles, we study the time-dependent behavior of both magnetization and microstructures of the ferrofluid by changing values of two parameters, the shear rate strength and frequency of oscillatory shear flow. Simulation results show that there are three different dynamical regimes for the chain clusters dynamics, depending on these two parameters. Scaling behavior of the asymptotic magnetization is also observed for a certain range of parameters.     

Non-Gaussian normal diffusion in low dimensional systems

Brownian particles suspended in disordered crowded environments often exhibit non-Gaussian normal diffusion (NGND), whereby their displacements grow with mean square proportional to the observation time and non-Gaussian statistics. Their distributions appear to decay almost exponentially according to “universal” laws largely insensitive to the observation time. This effect is generically attributed to slow environmental fluctuations, which perturb the local configuration of the suspension medium. To investigate the microscopic mechanisms responsible for the NGND phenomenon, we study Brownian diffusion in low dimensional systems, like the free diffusion of ellipsoidal and active particles, the diffusion of colloidal particles in fluctuating corrugated channels and Brownian motion in arrays of planar convective rolls. NGND appears to be a transient effect related to the time modulation of the instantaneous particle’s diffusivity, which can occur even under equilibrium conditions. Consequently, we propose to generalize the definition of NGND to include transient displacement distributions which vary continuously with the observation time. To this purpose, we provide a heuristic one-parameter function, which fits all time-dependent transient displacement distributions corresponding to the same diffusion constant. Moreover, we reveal the existence of low dimensional systems where the NGND distributions are not leptokurtic (fat exponential tails), as often reported in the literature, but platykurtic (thin sub-Gaussian tails), i.e., with negative excess kurtosis. The actual nature of the NGND transients is related to the specific microscopic dynamics of the diffusing particle.     

Effect of sample shape on nonlinear magnetization dynamics under an external magnetic field

Effect of sample shape on the nonlinear collective dynamics of magnetic moments in the presence of oscillating and constant external magnetic fields is studied using the Landau–Lifshitz–Gilbert (LLG) approach. The uniformly magnetized sample is considered to be an ellipsoidal axially symmetric particle described by demagnetization factors and uniaxial crystallographic anisotropy formed some angle with an applied field direction. It is investigated as to how the change in particle shape affects its nonlinear magnetization dynamics. To produce a regular study, all results are presented in the form of bifurcation diagrams for all sufficient dynamics regimes of the considered system. In this paper, we show that the sample's (particle's) shape and its orientation with respect to the external field (system configuration) determine the character of magnetization dynamics: deterministic behavior and appearance of chaotic states. A simple change in the system's configuration or in the shapes of its parts can transfer it from chaotic to periodic or even static regime and back. Moreover, the effect of magnetization precession stall and magnetic moments alignment parallel or antiparallel to the external oscillating field is revealed and the way of control of such “polarized” states is found. Our results suggest that varying the particle's shape and fields’ geometry may provide a useful way of magnetization dynamics control in complex magnetic systems.     

The magneto-optical properties of an ensemble of ellipsoidal dielectric particles in a magnetic fluid

The paper deals with an analytical investigation of magnetic birefringence in a dilute suspension of ellipsoidal dielectric particles in a magnetic fluid. The major axes of particles tend to line up along the field because of the difference in the “demagnetizing” coefficients along and across the ellipsoid axis, which brings about a multiple increase in the optical anisotropy of the system. Formulas are derived which describe the field dependence of magnetization of the system and of the difference between the refractive indices for ordinary and extraordinary rays. It is demonstrated that, given the bulk concentration of impurity particles of several percent, the magnetization of the system varies insignificantly, while the birefringence signal may increase by two orders of magnitude.     

A modified analytical model of the alkali-metal atomic magnetometer employing longitudinal carrier field

Alkali-metal atomic magnetometers employing longitudinal carrier magnetic field have ultrahigh sensitivity to measure transverse magnetic fields and have been applied in a variety of precise-measurement science and technologies. In practice, the magnetometer response is not rigorously proportional to the measured transverse magnetic fields and the existing fundamental analytical model of this magnetometer is effective only when the amplitudes of the measured fields are very small. In this paper, we present a modified analytical model to characterize the practical performance of the magnetometer more definitely. We find out how the longitudinal magnetization of the alkali metal atoms vary with larger transverse fields. The linear-response capacity of the magnetometer is determined by these factors: the amplitude and frequency of the longitudinal carrier field, longitudinal and transverse spin relaxation time of the alkali spins and rotation frequency of the transverse fields. We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method and simulation experiments are conducted to verify the validity and correctness of the proposed modified model. This model can be helpful for measuring larger fields more accurately and configuring a desirable magnetometer with proper linear range.